#include <cstdio>

#pragma warning(disable:4996)

#define INF 987654321
#define CLOCK 16

using namespace std;

int relatedClocks[10][5] = {
    {0,1,2,-1,-1},
    { 3, 7, 9, 11, -1 },
    { 4, 10, 14, 15 -1 },
    { 0, 4, 5, 6, 7 },
    { 6, 7, 8, 10, 12 },
    { 0, 2, 14, 15, -1 },
    { 3, 14, 15, -1, -1 },
    { 4, 5, 7, 14, 15 },
    { 1, 2, 3, 4, 5 },
    { 3, 4, 5, 9, 13 }
};

int all12(int clocks[CLOCK]){
    int count12 = 0;
    for (int i = 0; i < CLOCK; i++){
        if (clocks[i] == 12) count12++;
    }
    if (count12 == CLOCK) return 1;
    return 0;
}

void moveClocks(int clocks[CLOCK], int switches[10], int sw_pos, int type){
    if (type == 1){
        for (int move = 0; move < switches[sw_pos]; move++){
            int selectedClock;
            for (int i = 0; i < 5; i++){
                selectedClock = relatedClocks[sw_pos][i];
                if (selectedClock != -1){
                    clocks[selectedClock] += 3;
                    if (clocks[selectedClock] > 12) clocks[selectedClock] -= 12;
                }
            }
        }
    }
    else{
        for (int move = 0; move < switches[sw_pos]; move++){
            int selectedClock;
            for (int i = 0; i < 5; i++){
                selectedClock = relatedClocks[sw_pos][i];
                if (selectedClock != -1){
                    clocks[selectedClock] -= 3;
                    if (clocks[selectedClock] < 1) clocks[selectedClock] += 12;
                }
            }
        }
    }
}

int onSwitches(int switches[10]){
    int os = 0;
    for (int i = 0; i < 10; i++){
        os += switches[i];
    }
    return os;
}

int min(int a, int b){
    return a <= b ? a : b;
}
//디버깅용
void showClocks(int clocks[CLOCK], int type){
    if (type == 1) printf("moving\t");
    else printf("reversing\t");
    for (int i = 0; i < CLOCK; i++){
        printf("%d\t", clocks[i]);
    }
    printf("\n");
}

int syncClocks(int clocks[CLOCK], int switches[10], int sw_pos){

    // 스위치 경우의 수 완전탐색
    // 검사

    if (sw_pos == 10){
        //printf("\n");
        if (all12(clocks))
            return onSwitches(switches);
        else
            return INF;
    }

    int ret = INF;

    for (int times = 0; times < 4; times++){
        switches[sw_pos] = times;
        //printf("%d\t", times);
        moveClocks(clocks, switches, sw_pos, 1);
        //showClocks(clocks, 1);
        ret = min(ret, syncClocks(clocks, switches, sw_pos + 1));
        moveClocks(clocks, switches, sw_pos, -1); // 원상복귀
        //showClocks(clocks, -1);
    }

    return ret;
}

int main(void){

    int tc;
    int clocks[CLOCK];  

    scanf("%d", &tc);

    for (int i = 0; i < tc; i++){
        int switches[10] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 };
        int ret;
        for (int j = 0; j < CLOCK; j++){
            scanf("%d", &clocks[j]);
        }
        ret = syncClocks(clocks, switches, 0);
        if (ret == INF) ret = -1;
        printf("%d\n", ret);
    }

    return 0;
}